I always think of "edge" in purely statistical, probabilistic terms.
I'd define it as "the degree of confidence with which you know that backtesting and/or forward-testing have reliably demonstrated that it's a method which consistently wins more collectively from its winning trades than it collectively loses from its losing trades".
I hear you ... but "all those other things" you're thinking of, the practicalities, skill-set, and so on, all of which are equally necessary, I think of as "technique", not "edge".
I'd say that the trade-management rules ought to be part of the definition of the method, part of the fixed parameters that form the determination of whether or not it has the statistically proven "edge" in the first place.
You need lots and lots of different things in place, to be able to trade successfully over the long-term, and any one of them being missing can prevent that from happening. But I think it's fair to say that "lack of a (statistically proven) edge" is a very common reason - perhaps the most common single reason - for aspiring traders not making it.